Hello dear community,
I want to solve a partial differential equation that has a negative value only in the center of the area. the initial condition is that all space is equal to 1 at t = 0. The 2 edge conditions are that they are constant and equal to 1 at all times, but the other 2 edge conditions must be that the second derivative is equal to zero.
This is the code I am testing. giving me an error due to the derivative I use for the boundary conditions. How can I correctly include this condition for the edge?
a=2;
Sol = NDSolveValue[
{D[h[t, x, y], t] == (D[h[t, x, y], x, x] + D[h[t, x, y], y, y]) - If[x == 0 && y == 0, a, 0],
h[0, x, y] == 1,
h[t, -1, y] == 1,
h[t, 1, y] == 1,
D[h[t, x, y], x, x] == 0 /. y -> -1,
D[h[t, x, y], x, x] == 0 /. y -> +1
},
h, {t, 0, 2000}, {x, -1, 1}, {y, -1, 1}
];
Kind regards.